ABSTRACT
Many of the macromolecules of living organisms are filamentous. Not only are they a striking visual feature within cells, but their structure is intimately tied to the ways in which such molecules are used in cells. The representation of geometric structures as networks of one-dimensional elements is a perspective of great power and applicability. Biological filaments are characterized by one dimension that is much greater than their transverse dimensions. For example, in the case of the bacterial flagellum, the structure has a length in excess of microns with a diameter that is measured in only tens of nanometers. The competition between thermal fluctuations and the energetic cost associated with beam bending is succinctly captured in the emergence of a single length scale, namely, the persistence length. An alternative view of the persistence length is to think of biological polymers from the standpoint of the geometry of space curves.
